Solve x^4y^4-9x^2y^2

$${ x }^{ 4 } { y }^{ 4 } -9 { x }^{ 2 } { y }^{ 2 }$$

Factor

$$x^{2}y^{2}\left(xy-3\right)\left(xy+3\right)$$

Solution Steps

Factor out x^{2}y^{2}.

$$x^{2}y^{2}\left(x^{2}y^{2}-9\right)$$

Consider x^{2}y^{2}-9. Rewrite x^{2}y^{2}-9 as \left(xy\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(xy-3\right)\left(xy+3\right)$$

Rewrite the complete factored expression.

$$x^{2}y^{2}\left(xy-3\right)\left(xy+3\right)$$

Evaluate

$$\left(xy\right)^{2}\left(\left(xy\right)^{2}-9\right)$$